[BM] Belyakov É. B. and Mart'yanov V. I., Universal theories of integers and the extended Bliznetsov hypothesis, Algebra i Logika, vol. 22 (1983), pp. 26–34; English translation, Algebra and Logik, vol. 22 (1983), pp. 19–26.

[B1] Büchi J. R., Weak second-order arithmetic and finite automata, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 6 (1960), pp. 66–92.

[B2] Büchi J. R., On a decision method in restricted second order arithmetic, Logic, Methodology, and Philosophy of Science, Proceedings of the 1960 Congress, Stanford University Press, Stanford, California, pp. 1–11.

[BL] Büchi J. R. and Landweber L., Definability in the monadic second-order theory of successor, this Journal, vol. 34 (1969), pp. 166–170.

[C] Choueka Y., Theories of automata on ω-tapes: a simplified approach, Journal of Computer and System Sciences, vol. 8 (1974), pp. 117–141.

[D] Dickson L. E., A new extension of Dirichlet's theorem on prime numbers, Messenger of Mathematics, vol. 33 (1903–1904), pp. 155–161.

[E] Elgot C. C., Decision problems of finite automata design and related arithmetics, Transactions of the American Mathematical Society, vol. 98 (1961), pp. 21–51.

[ER] Elgot C. C. and Rabin M. O., Decidability and undecidability of second (first) order theory of (generalized) successor, this Journal, vol. 31 (1966), pp. 169–181.

[HR] Halberstam H. and Richert H. E., Sieve methods, Academic Press, Orlando, Florida, 1974.

[HU] Hopcroft J. E. and Ullman J. D., Introduction to automata theory, languages, and computation, Addison-Wesley, Reading, Massachusetts, 1979.

[Mc1] McNaughton R., review of [B1], this Journal, vol. 28 (1963), pp. 100–102.

[Mc2] McNaughton R., Testing and generating infinite sequences by a finite automaton, Information and Control, vol. 9 (1966), pp. 521–530.

[Mu] Muller D. E., Infinite sequences and finite machines, Switching circuit theory and logical design: proceedings of the fourth annual symposium, Institute of Electrical and Electronic Engineers, New York, 1963, pp. 3–16.

[Pr] Presburger M., Über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt, Comptes Rendus du I^{er} Congrès des Mathématiciens des Pays Slaves, Warszawa, 1929. pp. 92–101.

[Pu] Putman H., Decidability and essential undecidability, this Journal, vol. 22 (1957), pp. 39–54.

[R1] Rabin M. O., Decidability of second-order theories and automata on infinite trees, Transactions of the American Mathematical Society, vol. 141 (1969), pp. 1–35.

[R2] Rabin M. O., Automata on infinite objects and Church's problem, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 13, American Mathematical Society, Providence, Rhode Island, 1972.

[SS] Schinzel A. and Sierpinski W., Sur certaines hypothèses concernant les nomhres premiers, Acta Arithmetica, vol. 4 (1958), pp. 185–208 (see also ibid 5 (1959), p. 259 for a correction).

[Schi] Schinzel A., Remarks on the paper, “Sur certaines hypothèses concernant les nombres premiers”, Acta Arithmetica, vol. 7 (1961), pp. 1–8.

[Schn] Schnirelmann L., Über additive Eigenschaften von Zahlen, Mathematische Annalen, vol. 107 (1933), pp. 649–690.

[Se1] Semënov A. L., On certain extensions of the arithmetic of addition of natural numbers, Mathematics of the USSR—Izvestiya, vol. 15 (1980), pp. 401–419.

[Se2] Semënov A. L., Logical theories of one-place functions on the set of natural numbers, Izvestiya Akademii Nauk SSSR Seriya Mathematicheskaya, vol. 47 (1983), pp. 623–658; English translation, **Mathematics of the USSR—Izvestiya**, vol. 22 (1984), pp. 587–618.

[Se3] Semënov A. L., Decidability of monadic theories, Springer Lecture Notes in Computer Science, vol. 176, Springer-Verlag, Berlin, 1984, pp. 162–175.

[Si] Siefkes D., Decidable extensions of monadic second order successor arithmetic, Automaten-theorie und formate Sprachen (Dörr J. and Hotz G., editors), Berichte aus dem mathematischen Forschungsinstitut Oberwolfach, vol. 3 (1970), pp. 441–472.

[T1] Thomas W., The theory of successor with an extra predicate, Mathematische Annalen, vol. 237 (1978), pp. 121–132.

[T2] Thomas W., On the bounded monadic theory of well-ordered structures, this Journal, vol. 45 (1980), pp. 334–338.

[T3] Thomas W., A combinatorial approach to the theory of ω-automata, Information and Control, vol. 48 (1981), pp. 261–283.

[W] Woods A. R., Some problems in logic and number theory, and their connections, **Ph.D. thesis**, University of Manchester, Manchester, 1981.